Seeing someone asking PRT's question but no one answered, plus herself in bed today, practice typing
Note: 1. Some English do not know how to translate.
2. I only talk about it (if you want to talk about, the papers are definitely less.)
1. What is the first Spherical Harmonics?
They are actually a orthogonal Basis function represented by Legendre Polynomials. We can simulate a function by scaling and combining it (Scale & Combine) Functions. But before the simulation, we must first project the original function to the Basis function so that we can get its Coefficients (coefficient), and we can use its coefficient and the Basis Function to reducing the original function. We can imagine orthogonal Basis functions (1, 0) and (0, 1), the coefficient is (x, 0) and (0, y), assuming the original vector is (x, y). The coefficient (x, 0) = (x, y) * (1, 0), (0, y) = (x, y) * (0, 1). Then restore (x, y) = (x, 0) * (1, 0) (0, y) * (0, 1)
And for orthogonal Basis functions, they have a characteristic: through the coefficient of the original function and another original function, we can achieve the points of the two original functions! This is one of the most important reasons why we use it as light simulation. (Note: Only for orthogonal Basis functions!) Another reason is that its definition domain is within the spherical range. (Our classic rendering formula is to define the domain)
PS. In fact, Spherical Harmonics is more applied to quantum mechanics and COMPUTASTRY.
2. How do you use them to simulate light?
We know that when you want to use the rendering formula to simulate the light, there is a tricky problem, that is, points. But through Spherical Harmonics, we can simplify points into addition and multiplication, that is, a few points! (In the end, several ORDERs on Spherical Harmonics)
So we need two coefficients, one is the coefficient of the BRDF () × COS () × V () function, and the other is L () is also the coefficient of the light function. In the pre-rendering phase, we get those functions Project, and you can use a few fast points when rendering. (This is why it is so fast.)
PS. Use the Monte Carlo Raytracing / Integration when BRDF () × COS () × V (). (V () is a Visibility Function (visible letter function))
PS. Generally speaking, when using the SH-simulated light, we only use Perfect Diffuse's BRDF, its BRDF is very simple, that is, Albedo (Color) / Pi.
3. How do you use them to simulate your dynamic light?
There is also a reason why we use SH to simulate light is their rotationally invariant (rotation invariance). With this nature, when the single light source is rotated, we only need to rotate its coefficient, without rotating L (). If they don't have this nature, each of the light sources is rotated, we have to re-project L () once, and Projection is very time.
Ivanic / Ruedenberg Sh Rotation and Choi. Sh Rotation is two comparatively universal rotation methods. (I don't know what DX is used) PS. Need to pay attention to the rotating SH factor is very difficult (it is a nightmare!) (Exaggerated
)
To Be Continued
